Discontinuous Galerkin Methods for the Biharmonic Problem

This work is concerned with the design and analysis of hp-version discontinuous Galerkin (DG) finite element methods for boundary-value problems involving the biharmonic operator. The first part extends the unified approach of Arnold, Brezzi, Cockburn & Marini (SIAM J. Numer. Anal. 39, 5 (2001/02), 1749-1779) developed for the Poisson problem, to the design of DG methods via an appropriate choice of numerical flux functions for fourth order problems; as an example we retrieve the interior penalty DG method developed by Suli & Mozolevski (Comput. Methods Appl. Mech. Engrg. 196, 13-16 (2007), 1851-1863). The second part of this work is concerned with a new a-priori error analysis of the hp-version interior penalty DG method, when the error is measured in terms of both the energy-norm and L2-norm, as well certain linear functionals of the solution, for elemental polynomial degrees $p\ge 2$. Also, provided that the solution is piecewise analytic in an open neighbourhood of each element, exponential convergence is also proven for the p-version of the DG method. The sharpness of the theoretical developments is illustrated by numerical experiments.

Effort-reward imbalance at work and the co-occurrence of lifestyle risk factors: cross-sectional survey in a sample of 36,127 public sector employees

Background In occupational life, a mismatch between high expenditure of effort and receiving few rewards may promote the co-occurrence of lifestyle risk factors, however, there is insufficient evidence to support or refute this hypothesis. The aim of this study is to examine the extent to which the dimensions of the Effort-Reward Imbalance (ERI) model – effort, rewards and ERI – are associated with the co-occurrence of lifestyle risk factors. Methods Based on data from the Finnish Public Sector Study, cross-sectional analyses were performed for 28,894 women and 7233 men. ERI was conceptualized as a ratio of effort and rewards. To control for individual differences in response styles, such as a personal disposition to answer negatively to questionnaires, occupational and organizational -level ecological ERI scores were constructed in addition to individual-level ERI scores. Risk factors included current smoking, heavy drinking, body mass index ≥25 kg/m2, and physical inactivity. Multinomial logistic regression models were used to estimate the likelihood of having one risk factor, two risk factors, and three or four risk factors. The associations between ERI and single risk factors were explored using binary logistic regression models. Results After adjustment for age, socioeconomic position, marital status, and type of job contract, women and men with high ecological ERI were 40% more likely to have simultaneously ≥3 lifestyle risk factors (vs. 0 risk factors) compared with their counterparts with low ERI. When examined separately, both low ecological effort and low ecological rewards were also associated with an elevated prevalence of risk factor co-occurrence. The results obtained with the individual-level scores were in the same direction. The associations of ecological ERI with single risk factors were generally less marked than the associations with the co-occurrence of risk factors. Conclusion This study suggests that a high ratio of occupational efforts relative to rewards may be associated with an elevated risk of having multiple lifestyle risk factors. However, an unexpected association between low effort and a higher likelihood of risk factor co-occurrence as well as the absence of data on overcommitment (and thereby a lack of full test of the ERI model) warrant caution in regard to the extent to which the entire ERI model is supported by our evidence.

Coarse-graining and renormalisation group methods for the elucidation of the kinetics of complex nucleation and growth processes

We review our work on generalisations of the Becker-Doring model of cluster-formation as applied to nucleation theory, polymer growth kinetics, and the formation of upramolecular structures in colloidal chemistry. One valuable tool in analysing mathematical models of these systems has been the coarse-graining approximation which enables macroscopic models for observable quantities to be derived from microscopic ones. This permits assumptions about the detailed molecular mechanisms to be tested, and their influence on the large-scale kinetics of surfactant self-assembly to be elucidated. We also summarise our more recent results on Becker-Doring systems, notably demonstrating that cross-inhibition and autocatalysis can destabilise a uniform solution and lead to a competitive environment in which some species flourish at the expense of others, phenomena relevant in models of the origins of life.